![\huge \displaystyle\sf\lim\limits_{x\to\infty}\sqrt[x]{\dfrac{x!}{x^{x}}}](https://tex.z-dn.net/?f=%5Chuge+%5Cdisplaystyle%5Csf%5Clim%5Climits_%7Bx%5Cto%5Cinfty%7D%5Csqrt%5Bx%5D%7B%5Cdfrac%7Bx%21%7D%7Bx%5E%7Bx%7D%7D%7D "\huge \displaystyle\sf\lim\limits_{x\to\infty}\sqrt[x]{\dfrac{x!}{x^{x}}}")
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Answers
Given :
The Ratio of present ages of arti and arjun is 5:3 .
Arti's age is 45 yrs .
To Find :
Present age of Arjun .
Solution :
\longmapsto\tt{Let\:present\:age\:of\:Arti\:be=5x}⟼LetpresentageofArtibe=5x
\longmapsto\tt{Let\:present\:age\:of\:Arjun\:be=3x}⟼LetpresentageofArjunbe=3x
As Given that Age of Arti is 45 . So ,
\longmapsto\tt{5x=45}⟼5x=45
\longmapsto\tt{x=\cancel\dfrac{45}{5}}⟼x=
5
45
\longmapsto\tt\bf{x=9}⟼x=9
Value of x is 9 .
Therefore :
\longmapsto\tt{Present\:age\:of\:Arjun=3(9)}⟼PresentageofArjun=3(9)
\longmapsto\tt\bf{27\:years}
Given :
The Ratio of present ages of arti and arjun is 5:3 .
Arti's age is 45 yrs .
To Find :
Present age of Arjun .
Solution :
\longmapsto\tt{Let\:present\:age\:of\:Arti\:be=5x}⟼LetpresentageofArtibe=5x
\longmapsto\tt{Let\:present\:age\:of\:Arjun\:be=3x}⟼LetpresentageofArjunbe=3x
As Given that Age of Arti is 45 . So ,
\longmapsto\tt{5x=45}⟼5x=45
\longmapsto\tt{x=\cancel\dfrac{45}{5}}⟼x=
5
45
\longmapsto\tt\bf{x=9}⟼x=9
Value of x is 9 .
Therefore :
\longmapsto\tt{Present\:age\:of\:Arjun=3(9)}⟼PresentageofArjun=3(9)
\longmapsto\tt\bf{27\:years}